Controllability of 3D incompressible Euler equations by a finite-dimensional external force

Hayk Nersisyan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 3, page 677-694
  • ISSN: 1292-8119

Abstract

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In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force.

How to cite

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Nersisyan, Hayk. "Controllability of 3D incompressible Euler equations by a finite-dimensional external force." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 677-694. <http://eudml.org/doc/250730>.

@article{Nersisyan2010,
abstract = { In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force. },
author = {Nersisyan, Hayk},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; 3D incompressible Euler equations; Agrachev-Sarychev method; controllability},
language = {eng},
month = {7},
number = {3},
pages = {677-694},
publisher = {EDP Sciences},
title = {Controllability of 3D incompressible Euler equations by a finite-dimensional external force},
url = {http://eudml.org/doc/250730},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Nersisyan, Hayk
TI - Controllability of 3D incompressible Euler equations by a finite-dimensional external force
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/7//
PB - EDP Sciences
VL - 16
IS - 3
SP - 677
EP - 694
AB - In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force.
LA - eng
KW - Controllability; 3D incompressible Euler equations; Agrachev-Sarychev method; controllability
UR - http://eudml.org/doc/250730
ER -

References

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  11. S.S. Rodrigues, Navier–Stokes equation on the rectangle: controllability by means of low mode forcing. J. Dyn. Control Syst.12 (2006) 517–562.  
  12. A. Shirikyan, Approximate controllability of three-dimensional Navier–Stokes equations. Comm. Math. Phys.266 (2006) 123–151.  
  13. A. Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire24 (2007) 521–537.  
  14. A. Shirikyan, Euler equations are not exactly controllable by a finite-dimensional external force. Physica D237 (2008) 1317–1323.  
  15. M.E. Taylor, Partial Differential Equations, III. Springer-Verlag, New York (1996).  
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